Could anyone suggest a tool (a Web app or for OS X) that has the following function?
Given a word → generate all its related words (synonyms) and show its connections (how these words are related).
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WordWeb will meet your needs and requirements.
It is not open-source, but you indicated this is only preferable, and not a requirement.
WordWeb will show you related words, and how they are related to each other. This includes synonyms, antonyms, similar words, types of, types, parts of, and parts.